Question

A random sample of size 4 is taken with replacement from a population with population mean of 12 and population variance of 8. [What is the standard deviation of the sampling distribution]. 

Answer 1

Standard deviation of the sampling distribution will be $\sigma_x={\frac {\sigma} {\sqrt n}={\frac {\sqrt 8} {\sqrt 4}}}=\sqrt 2$

In the formula above n is sample size and $\sigma$ is population standard deviation